Best Known (63−25, 63, s)-Nets in Base 64
(63−25, 63, 513)-Net over F64 — Constructive and digital
Digital (38, 63, 513)-net over F64, using
- t-expansion [i] based on digital (28, 63, 513)-net over F64, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
(63−25, 63, 1366)-Net in Base 64 — Constructive
(38, 63, 1366)-net in base 64, using
- base change [i] based on digital (29, 54, 1366)-net over F128, using
- 1282 times duplication [i] based on digital (27, 52, 1366)-net over F128, using
- net defined by OOA [i] based on linear OOA(12852, 1366, F128, 25, 25) (dual of [(1366, 25), 34098, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(12852, 16393, F128, 25) (dual of [16393, 16341, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(12852, 16396, F128, 25) (dual of [16396, 16344, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,10]) [i] based on
- linear OA(12849, 16385, F128, 25) (dual of [16385, 16336, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(12841, 16385, F128, 21) (dual of [16385, 16344, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(1283, 11, F128, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,128) or 11-cap in PG(2,128)), using
- discarding factors / shortening the dual code based on linear OA(1283, 128, F128, 3) (dual of [128, 125, 4]-code or 128-arc in PG(2,128) or 128-cap in PG(2,128)), using
- Reed–Solomon code RS(125,128) [i]
- discarding factors / shortening the dual code based on linear OA(1283, 128, F128, 3) (dual of [128, 125, 4]-code or 128-arc in PG(2,128) or 128-cap in PG(2,128)), using
- construction X applied to C([0,12]) ⊂ C([0,10]) [i] based on
- discarding factors / shortening the dual code based on linear OA(12852, 16396, F128, 25) (dual of [16396, 16344, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(12852, 16393, F128, 25) (dual of [16393, 16341, 26]-code), using
- net defined by OOA [i] based on linear OOA(12852, 1366, F128, 25, 25) (dual of [(1366, 25), 34098, 26]-NRT-code), using
- 1282 times duplication [i] based on digital (27, 52, 1366)-net over F128, using
(63−25, 63, 8587)-Net over F64 — Digital
Digital (38, 63, 8587)-net over F64, using
(63−25, 63, large)-Net in Base 64 — Upper bound on s
There is no (38, 63, large)-net in base 64, because
- 23 times m-reduction [i] would yield (38, 40, large)-net in base 64, but